This unit discusses differentiable functions and some important properties that differentiable functions possess. It defines what it means for a function to be differentiable at a point and establishes some of the basic differentiable functions. It also considers functions that can be differentiated more than once. It studies the properties of functions that are differentiable on an interval, and establishes some useful results about derivatives which can also be described geometrically. Finally it covers I'Hopital's Rule, a result which enables us to find certain limits of a form for which the Quotient Rule fails.The video programme, I'Hopital's Rule, associated with this unit is available on DVD00126 (order code M208/DVD02).